Abstract: A vehicle fuel system has on-board diagnostics for leak testing with correction for different operating conditions. An electronic control unit (ECU) is arranged to carry out a periodic two stage leak test, when the engine is running. Stage A includes evacuation of the fuel tank, monitoring bleedup and recording the pressure rise dP_A over a predetermined period A following increase of pressure to a predetermined value p2. Stage B includes measuring the amount dP_B by which the pressure in the tank rises above atmospheric due to vapor generation over a predetermined period B following venting and closure fuel system. The ECU calculates a value X representative of leakage from the difference between dP_A and dP_B using a scaling factor K dependent on measured values of operating conditions, which may include fuel level/fuel tank free volume and/or ambient temperature.